Drive systems of the type referred to above using a pin drive chain arranged on the face conveyor and laid in a chain duct have been known in numerous designs for a long time and are customary in underground coal mining (DE 36 22 110 C2, DE 29 38 408 C2, DE 29 38 408 C2, DE 44 23 925 A1, DE 29 38 446 A1, DE 28 29 011 B1). In this case, it is usual to attach the pin drive chain, arranged along the chain conveyor in a chain duct which is open at the top, by its chain ends to the conveyor in the end regions thereof. During travelling and excavation operation of the cutting machine which is guided along the face conveyor and straddles the latter in the manner of a portal, the chain section of the pin drive chain which lies in front of the cutting machine in the direction of travel thereof is subjected to tensile loading and is consequently held taut in its course, whereas the chain may be slack in the chain section of the pin drive chain located behind the cutting machine. In view of the usually curved course of the face conveyor, this may also lead to wear on the chain and its guiding and possibly also to malfunctions.